LMFDB - Embedded newform 1445.2.d.g.866.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1445,2,Mod(866,1445)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1445, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1445.866");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1445 = 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1445.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.5383830921$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 83x^{8} + 152x^{6} + 111x^{4} + 22x^{2} + 1 $ x^12 + 18x^10 + 83x^8 + 152x^6 + 111x^4 + 22*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			866.4
Root			$-1.52346i$ of defining polynomial
Character	$\chi$	$=$	1445.866
Dual form			1445.2.d.g.866.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.07061 q^{2} +2.52346i q^{3} +2.28744 q^{4} +1.00000i q^{5} -5.22511i q^{6} -0.368961i q^{7} -0.595174 q^{8} -3.36786 q^{9} -2.07061i q^{10} +2.49810i q^{11} +5.77226i q^{12} +4.68778 q^{13} +0.763976i q^{14} -2.52346 q^{15} -3.34250 q^{16} +6.97354 q^{18} +7.16938 q^{19} +2.28744i q^{20} +0.931060 q^{21} -5.17260i q^{22} -6.70055i q^{23} -1.50190i q^{24} -1.00000 q^{25} -9.70657 q^{26} -0.928289i q^{27} -0.843976i q^{28} +6.78165i q^{29} +5.22511 q^{30} +4.81801i q^{31} +8.11138 q^{32} -6.30387 q^{33} +0.368961 q^{35} -7.70378 q^{36} -1.93935i q^{37} -14.8450 q^{38} +11.8294i q^{39} -0.595174i q^{40} +2.35972i q^{41} -1.92786 q^{42} +11.7105 q^{43} +5.71425i q^{44} -3.36786i q^{45} +13.8743i q^{46} +1.65317 q^{47} -8.43468i q^{48} +6.86387 q^{49} +2.07061 q^{50} +10.7230 q^{52} +6.81536 q^{53} +1.92213i q^{54} -2.49810 q^{55} +0.219596i q^{56} +18.0917i q^{57} -14.0422i q^{58} +0.484372 q^{59} -5.77226 q^{60} +6.88307i q^{61} -9.97624i q^{62} +1.24261i q^{63} -10.1105 q^{64} +4.68778i q^{65} +13.0529 q^{66} -1.87478 q^{67} +16.9086 q^{69} -0.763976 q^{70} +1.71958i q^{71} +2.00446 q^{72} -0.286310i q^{73} +4.01564i q^{74} -2.52346i q^{75} +16.3995 q^{76} +0.921703 q^{77} -24.4942i q^{78} -5.38563i q^{79} -3.34250i q^{80} -7.76109 q^{81} -4.88608i q^{82} -9.94985 q^{83} +2.12974 q^{84} -24.2479 q^{86} -17.1132 q^{87} -1.48680i q^{88} +4.30781 q^{89} +6.97354i q^{90} -1.72961i q^{91} -15.3271i q^{92} -12.1581 q^{93} -3.42308 q^{94} +7.16938i q^{95} +20.4688i q^{96} -12.7460i q^{97} -14.2124 q^{98} -8.41327i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + 12 q^{4} - 12 q^{8} - 4 q^{9} - 8 q^{15} + 4 q^{16} + 28 q^{18} + 24 q^{19} + 16 q^{21} - 12 q^{25} + 24 q^{26} + 8 q^{30} + 12 q^{32} - 16 q^{33} + 16 q^{35} + 20 q^{36} - 24 q^{38} + 16 q^{42}+ \cdots - 44 q^{98}+O(q^{100}) $ 12 * q - 4 * q^2 + 12 * q^4 - 12 * q^8 - 4 * q^9 - 8 * q^15 + 4 * q^16 + 28 * q^18 + 24 * q^19 + 16 * q^21 - 12 * q^25 + 24 * q^26 + 8 * q^30 + 12 * q^32 - 16 * q^33 + 16 * q^35 + 20 * q^36 - 24 * q^38 + 16 * q^42 - 16 * q^43 + 48 * q^47 + 20 * q^49 + 4 * q^50 - 56 * q^52 + 32 * q^59 - 16 * q^60 - 28 * q^64 + 32 * q^66 - 8 * q^67 - 16 * q^70 - 20 * q^72 + 72 * q^76 - 48 * q^77 - 28 * q^81 - 40 * q^83 - 96 * q^86 - 48 * q^87 - 24 * q^89 - 72 * q^93 - 40 * q^94 - 44 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1445\mathbb{Z}\right)^\times$.

$n$	$581$	$1157$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.07061	−1.46414	−0.732072	−	0.681227i	$-0.761447\pi$
$2$	−2.07061	−1.46414	−0.732072	+	0.681227i	$0.761447\pi$
$3$	2.52346i	1.45692i	0.685087	+	0.728461i	$0.259764\pi$
$3$	2.52346i	1.45692i	−0.685087	+	0.728461i	$0.740236\pi$
$4$	2.28744	1.14372
$5$	1.00000i	0.447214i
$5$	1.00000i	0.447214i
$6$	− 5.22511i	− 2.13314i
$7$	− 0.368961i	− 0.139454i	−0.997566	−	0.0697271i	$-0.977787\pi$
$7$	− 0.368961i	− 0.139454i	0.997566	−	0.0697271i	$-0.0222129\pi$
$8$	−0.595174	−0.210426
$9$	−3.36786	−1.12262
$10$	− 2.07061i	− 0.654785i
$11$	2.49810i	0.753206i	0.926375	+	0.376603i	$0.122908\pi$
$11$	2.49810i	0.753206i	−0.926375	+	0.376603i	$0.877092\pi$
$12$	5.77226i	1.66631i
$13$	4.68778	1.30016	0.650078	−	0.759868i	$-0.274736\pi$
$13$	4.68778	1.30016	0.650078	+	0.759868i	$0.274736\pi$
$14$	0.763976i	0.204181i
$15$	−2.52346	−0.651555
$16$	−3.34250	−0.835626
$17$	0	0
$17$	0	0
$18$	6.97354	1.64368
$19$	7.16938	1.64477	0.822384	−	0.568933i	$-0.192644\pi$
$19$	7.16938	1.64477	0.822384	+	0.568933i	$0.192644\pi$
$20$	2.28744i	0.511487i
$21$	0.931060	0.203174
$22$	− 5.17260i	− 1.10280i
$23$	− 6.70055i	− 1.39716i	−0.715531	−	0.698581i	$-0.753815\pi$
$23$	− 6.70055i	− 1.39716i	0.715531	−	0.698581i	$-0.246185\pi$
$24$	− 1.50190i	− 0.306574i
$25$	−1.00000	−0.200000
$26$	−9.70657	−1.90361
$27$	− 0.928289i	− 0.178649i
$28$	− 0.843976i	− 0.159496i
$29$	6.78165i	1.25932i	0.776870	+	0.629661i	$0.216806\pi$
$29$	6.78165i	1.25932i	−0.776870	+	0.629661i	$0.783194\pi$
$30$	5.22511	0.953971
$31$	4.81801i	0.865341i	0.901552	+	0.432670i	$0.142429\pi$
$31$	4.81801i	0.865341i	−0.901552	+	0.432670i	$0.857571\pi$
$32$	8.11138	1.43390
$33$	−6.30387	−1.09736
$34$	0	0
$35$	0.368961	0.0623658
$36$	−7.70378	−1.28396
$37$	− 1.93935i	− 0.318827i	−0.987212	−	0.159413i	$-0.949040\pi$
$37$	− 1.93935i	− 0.318827i	0.987212	−	0.159413i	$-0.0509603\pi$
$38$	−14.8450	−2.40818
$39$	11.8294i	1.89422i
$40$	− 0.595174i	− 0.0941052i
$41$	2.35972i	0.368527i	0.982877	+	0.184263i	$0.0589900\pi$
$41$	2.35972i	0.368527i	−0.982877	+	0.184263i	$0.941010\pi$
$42$	−1.92786	−0.297476
$43$	11.7105	1.78584	0.892918	−	0.450218i	$-0.148654\pi$
$43$	11.7105	1.78584	0.892918	+	0.450218i	$0.148654\pi$
$44$	5.71425i	0.861456i
$45$	− 3.36786i	− 0.502051i
$46$	13.8743i	2.04565i
$47$	1.65317	0.241140	0.120570	−	0.992705i	$-0.461528\pi$
$47$	1.65317	0.241140	0.120570	+	0.992705i	$0.461528\pi$
$48$	− 8.43468i	− 1.21744i
$49$	6.86387	0.980553
$50$	2.07061	0.292829
$51$	0	0
$52$	10.7230	1.48701
$53$	6.81536	0.936162	0.468081	−	0.883686i	$-0.344946\pi$
$53$	6.81536	0.936162	0.468081	+	0.883686i	$0.344946\pi$
$54$	1.92213i	0.261568i
$55$	−2.49810	−0.336844
$56$	0.219596i	0.0293447i
$57$	18.0917i	2.39630i
$58$	− 14.0422i	− 1.84383i
$59$	0.484372	0.0630598	0.0315299	−	0.999503i	$-0.489962\pi$
$59$	0.484372	0.0630598	0.0315299	+	0.999503i	$0.489962\pi$
$60$	−5.77226	−0.745196
$61$	6.88307i	0.881286i	0.897682	+	0.440643i	$0.145250\pi$
$61$	6.88307i	0.881286i	−0.897682	+	0.440643i	$0.854750\pi$
$62$	− 9.97624i	− 1.26698i
$63$	1.24261i	0.156554i
$64$	−10.1105	−1.26381
$65$	4.68778i	0.581447i
$66$	13.0529	1.60670
$67$	−1.87478	−0.229041	−0.114520	−	0.993421i	$-0.536533\pi$
$67$	−1.87478	−0.229041	−0.114520	+	0.993421i	$0.536533\pi$
$68$	0	0
$69$	16.9086	2.03556
$70$	−0.763976	−0.0913126
$71$	1.71958i	0.204077i	0.994780	+	0.102038i	$0.0325365\pi$
$71$	1.71958i	0.204077i	−0.994780	+	0.102038i	$0.967464\pi$
$72$	2.00446	0.236228
$73$	− 0.286310i	− 0.0335101i	−0.999860	−	0.0167550i	$-0.994666\pi$
$73$	− 0.286310i	− 0.0335101i	0.999860	−	0.0167550i	$-0.00533355\pi$
$74$	4.01564i	0.466809i
$75$	− 2.52346i	− 0.291384i
$76$	16.3995	1.88115
$77$	0.921703	0.105038
$78$	− 24.4942i	− 2.77342i
$79$	− 5.38563i	− 0.605930i	−0.953002	−	0.302965i	$-0.902023\pi$
$79$	− 5.38563i	− 0.605930i	0.953002	−	0.302965i	$-0.0979766\pi$
$80$	− 3.34250i	− 0.373703i
$81$	−7.76109	−0.862343
$82$	− 4.88608i	− 0.539577i
$83$	−9.94985	−1.09214	−0.546069	−	0.837740i	$-0.683876\pi$
$83$	−9.94985	−1.09214	−0.546069	+	0.837740i	$0.683876\pi$
$84$	2.12974	0.232374
$85$	0	0
$86$	−24.2479	−2.61472
$87$	−17.1132	−1.83473
$88$	− 1.48680i	− 0.158494i
$89$	4.30781	0.456627	0.228314	−	0.973588i	$-0.426679\pi$
$89$	4.30781	0.456627	0.228314	+	0.973588i	$0.426679\pi$
$90$	6.97354i	0.735076i
$91$	− 1.72961i	− 0.181312i
$92$	− 15.3271i	− 1.59796i
$93$	−12.1581	−1.26073
$94$	−3.42308	−0.353064
$95$	7.16938i	0.735563i
$96$	20.4688i	2.08908i
$97$	− 12.7460i	− 1.29416i	−0.762424	−	0.647078i	$-0.775991\pi$
$97$	− 12.7460i	− 1.29416i	0.762424	−	0.647078i	$-0.224009\pi$
$98$	−14.2124	−1.43567
$99$	− 8.41327i	− 0.845565i
$100$	−2.28744	−0.228744
$101$	−9.08552	−0.904043	−0.452021	−	0.892007i	$-0.649297\pi$
$101$	−9.08552	−0.904043	−0.452021	+	0.892007i	$0.649297\pi$
$102$	0	0
$103$	4.77811	0.470801	0.235401	−	0.971898i	$-0.424360\pi$
$103$	4.77811	0.470801	0.235401	+	0.971898i	$0.424360\pi$
$104$	−2.79004	−0.273586
$105$	0.931060i	0.0908621i
$106$	−14.1120	−1.37068
$107$	− 2.85209i	− 0.275722i	−0.990452	−	0.137861i	$-0.955977\pi$
$107$	− 2.85209i	− 0.275722i	0.990452	−	0.137861i	$-0.0440227\pi$
$108$	− 2.12340i	− 0.204325i
$109$	− 9.44863i	− 0.905014i	−0.891761	−	0.452507i	$-0.850530\pi$
$109$	− 9.44863i	− 0.905014i	0.891761	−	0.452507i	$-0.149470\pi$
$110$	5.17260	0.493188
$111$	4.89387	0.464506
$112$	1.23325i	0.116532i
$113$	10.6789i	1.00459i	0.864698	+	0.502293i	$0.167510\pi$
$113$	10.6789i	1.00459i	−0.864698	+	0.502293i	$0.832490\pi$
$114$	− 37.4608i	− 3.50853i
$115$	6.70055	0.624830
$116$	15.5126i	1.44031i
$117$	−15.7878	−1.45958
$118$	−1.00295	−0.0923287
$119$	0	0
$120$	1.50190	0.137104
$121$	4.75949	0.432681
$122$	− 14.2522i	− 1.29033i
$123$	−5.95468	−0.536915
$124$	11.0209i	0.989707i
$125$	− 1.00000i	− 0.0894427i
$126$	− 2.57297i	− 0.229218i
$127$	−15.7315	−1.39595	−0.697974	−	0.716124i	$-0.745915\pi$
$127$	−15.7315	−1.39595	−0.697974	+	0.716124i	$0.745915\pi$
$128$	4.71221	0.416505
$129$	29.5510i	2.60182i
$130$	− 9.70657i	− 0.851322i
$131$	4.09160i	0.357485i	0.983896	+	0.178742i	$0.0572029\pi$
$131$	4.09160i	0.357485i	−0.983896	+	0.178742i	$0.942797\pi$
$132$	−14.4197	−1.25507
$133$	− 2.64522i	− 0.229370i
$134$	3.88194	0.335348
$135$	0.928289	0.0798944
$136$	0	0
$137$	−16.2144	−1.38529	−0.692644	−	0.721280i	$-0.743554\pi$
$137$	−16.2144	−1.38529	−0.692644	+	0.721280i	$0.743554\pi$
$138$	−35.0112	−2.98035
$139$	10.7071i	0.908168i	0.890959	+	0.454084i	$0.150033\pi$
$139$	10.7071i	0.908168i	−0.890959	+	0.454084i	$0.849967\pi$
$140$	0.843976	0.0713290
$141$	4.17172i	0.351322i
$142$	− 3.56059i	− 0.298798i
$143$	11.7105i	0.979285i
$144$	11.2571	0.938091
$145$	−6.78165	−0.563186
$146$	0.592838i	0.0490636i
$147$	17.3207i	1.42859i
$148$	− 4.43614i	− 0.364649i
$149$	11.1290	0.911719	0.455860	−	0.890052i	$-0.349332\pi$
$149$	11.1290	0.911719	0.455860	+	0.890052i	$0.349332\pi$
$150$	5.22511i	0.426629i
$151$	−16.0861	−1.30907	−0.654535	−	0.756032i	$-0.727135\pi$
$151$	−16.0861	−1.30907	−0.654535	+	0.756032i	$0.727135\pi$
$152$	−4.26702	−0.346101
$153$	0	0
$154$	−1.90849	−0.153790
$155$	−4.81801	−0.386992
$156$	27.0591i	2.16646i
$157$	2.63326	0.210157	0.105079	−	0.994464i	$-0.466491\pi$
$157$	2.63326	0.210157	0.105079	+	0.994464i	$0.466491\pi$
$158$	11.1516i	0.887170i
$159$	17.1983i	1.36392i
$160$	8.11138i	0.641261i
$161$	−2.47224	−0.194840
$162$	16.0702	1.26259
$163$	− 19.0937i	− 1.49554i	−0.663959	−	0.747769i	$-0.731125\pi$
$163$	− 19.0937i	− 1.49554i	0.663959	−	0.747769i	$-0.268875\pi$
$164$	5.39772i	0.421491i
$165$	− 6.30387i	− 0.490755i
$166$	20.6023	1.59905
$167$	3.98742i	0.308556i	0.988028	+	0.154278i	$0.0493051\pi$
$167$	3.98742i	0.308556i	−0.988028	+	0.154278i	$0.950695\pi$
$168$	−0.554142	−0.0427530
$169$	8.97524	0.690403
$170$	0	0
$171$	−24.1455	−1.84645
$172$	26.7871	2.04250
$173$	− 14.6078i	− 1.11061i	−0.831646	−	0.555307i	$-0.812601\pi$
$173$	− 14.6078i	− 1.11061i	0.831646	−	0.555307i	$-0.187399\pi$
$174$	35.4349	2.68631
$175$	0.368961i	0.0278908i
$176$	− 8.34991i	− 0.629398i
$177$	1.22229i	0.0918733i
$178$	−8.91981	−0.668568
$179$	−14.7452	−1.10211	−0.551054	−	0.834469i	$-0.685774\pi$
$179$	−14.7452	−1.10211	−0.551054	+	0.834469i	$0.685774\pi$
$180$	− 7.70378i	− 0.574206i
$181$	− 11.2615i	− 0.837059i	−0.908203	−	0.418529i	$-0.862546\pi$
$181$	− 11.2615i	− 0.837059i	0.908203	−	0.418529i	$-0.137454\pi$
$182$	3.58135i	0.265467i
$183$	−17.3692	−1.28397
$184$	3.98799i	0.293999i
$185$	1.93935	0.142584
$186$	25.1747	1.84590
$187$	0	0
$188$	3.78153	0.275797
$189$	−0.342503	−0.0249134
$190$	− 14.8450i	− 1.07697i
$191$	−21.4934	−1.55521	−0.777604	−	0.628754i	$-0.783565\pi$
$191$	−21.4934	−1.55521	−0.777604	+	0.628754i	$0.783565\pi$
$192$	− 25.5135i	− 1.84128i
$193$	1.42208i	0.102363i	0.998689	+	0.0511817i	$0.0162988\pi$
$193$	1.42208i	0.102363i	−0.998689	+	0.0511817i	$0.983701\pi$
$194$	26.3919i	1.89483i
$195$	−11.8294	−0.847123
$196$	15.7007	1.12148
$197$	17.4127i	1.24060i	0.784363	+	0.620302i	$0.212990\pi$
$197$	17.4127i	1.24060i	−0.784363	+	0.620302i	$0.787010\pi$
$198$	17.4206i	1.23803i
$199$	17.8876i	1.26802i	0.773325	+	0.634010i	$0.218592\pi$
$199$	17.8876i	1.26802i	−0.773325	+	0.634010i	$0.781408\pi$
$200$	0.595174	0.0420851
$201$	− 4.73093i	− 0.333694i
$202$	18.8126	1.32365
$203$	2.50217	0.175618
$204$	0	0
$205$	−2.35972	−0.164810
$206$	−9.89362	−0.689321
$207$	22.5665i	1.56848i
$208$	−15.6689	−1.08644
$209$	17.9098i	1.23885i
$210$	− 1.92786i	− 0.133035i
$211$	− 7.17979i	− 0.494277i	−0.968980	−	0.247139i	$-0.920510\pi$
$211$	− 7.17979i	− 0.494277i	0.968980	−	0.247139i	$-0.0794903\pi$
$212$	15.5897	1.07071
$213$	−4.33930	−0.297324
$214$	5.90557i	0.403697i
$215$	11.7105i	0.798651i
$216$	0.552493i	0.0375924i
$217$	1.77766	0.120675
$218$	19.5645i	1.32507i
$219$	0.722494	0.0488216
$220$	−5.71425	−0.385255
$221$	0	0
$222$	−10.1333	−0.680104
$223$	3.93334	0.263396	0.131698	−	0.991290i	$-0.457957\pi$
$223$	3.93334	0.263396	0.131698	+	0.991290i	$0.457957\pi$
$224$	− 2.99278i	− 0.199964i
$225$	3.36786	0.224524
$226$	− 22.1119i	− 1.47086i
$227$	− 3.47984i	− 0.230965i	−0.993310	−	0.115483i	$-0.963159\pi$
$227$	− 3.47984i	− 0.230965i	0.993310	−	0.115483i	$-0.0368414\pi$
$228$	41.3835i	2.74069i
$229$	−4.41164	−0.291529	−0.145765	−	0.989319i	$-0.546564\pi$
$229$	−4.41164	−0.291529	−0.145765	+	0.989319i	$0.546564\pi$
$230$	−13.8743	−0.914841
$231$	2.32588i	0.153032i
$232$	− 4.03626i	− 0.264993i
$233$	15.6666i	1.02635i	0.858284	+	0.513175i	$0.171531\pi$
$233$	15.6666i	1.02635i	−0.858284	+	0.513175i	$0.828469\pi$
$234$	32.6904	2.13704
$235$	1.65317i	0.107841i
$236$	1.10797	0.0721227
$237$	13.5904	0.882793
$238$	0	0
$239$	−6.59116	−0.426346	−0.213173	−	0.977014i	$-0.568380\pi$
$239$	−6.59116	−0.426346	−0.213173	+	0.977014i	$0.568380\pi$
$240$	8.43468	0.544456
$241$	4.38042i	0.282167i	0.989998	+	0.141084i	$0.0450587\pi$
$241$	4.38042i	0.282167i	−0.989998	+	0.141084i	$0.954941\pi$
$242$	−9.85506	−0.633507
$243$	− 22.3697i	− 1.43502i
$244$	15.7446i	1.00794i
$245$	6.86387i	0.438516i
$246$	12.3298	0.786121
$247$	33.6084	2.13845
$248$	− 2.86755i	− 0.182090i
$249$	− 25.1081i	− 1.59116i
$250$	2.07061i	0.130957i
$251$	4.30290	0.271597	0.135798	−	0.990736i	$-0.456640\pi$
$251$	4.30290	0.271597	0.135798	+	0.990736i	$0.456640\pi$
$252$	2.84240i	0.179054i
$253$	16.7387	1.05235
$254$	32.5739	2.04387
$255$	0	0
$256$	10.4639	0.653991
$257$	−10.5366	−0.657254	−0.328627	−	0.944460i	$-0.606586\pi$
$257$	−10.5366	−0.657254	−0.328627	+	0.944460i	$0.606586\pi$
$258$	− 61.1888i	− 3.80945i
$259$	−0.715544	−0.0444618
$260$	10.7230i	0.665012i
$261$	− 22.8397i	− 1.41374i
$262$	− 8.47213i	− 0.523410i
$263$	−13.6253	−0.840173	−0.420086	−	0.907484i	$-0.638000\pi$
$263$	−13.6253	−0.840173	−0.420086	+	0.907484i	$0.638000\pi$
$264$	3.75189	0.230913
$265$	6.81536i	0.418664i
$266$	5.47723i	0.335831i
$267$	10.8706i	0.665270i
$268$	−4.28844	−0.261958
$269$	15.6073i	0.951593i	0.879555	+	0.475796i	$0.157840\pi$
$269$	15.6073i	0.951593i	−0.879555	+	0.475796i	$0.842160\pi$
$270$	−1.92213	−0.116977
$271$	−9.66560	−0.587143	−0.293572	−	0.955937i	$-0.594844\pi$
$271$	−9.66560	−0.587143	−0.293572	+	0.955937i	$0.594844\pi$
$272$	0	0
$273$	4.36460	0.264158
$274$	33.5737	2.02826
$275$	− 2.49810i	− 0.150641i
$276$	38.6774	2.32810
$277$	1.35066i	0.0811535i	0.999176	+	0.0405767i	$0.0129195\pi$
$277$	1.35066i	0.0811535i	−0.999176	+	0.0405767i	$0.987080\pi$
$278$	− 22.1703i	− 1.32969i
$279$	− 16.2264i	− 0.971450i
$280$	−0.219596	−0.0131234
$281$	15.8582	0.946020	0.473010	−	0.881057i	$-0.343167\pi$
$281$	15.8582	0.946020	0.473010	+	0.881057i	$0.343167\pi$
$282$	− 8.63802i	− 0.514387i
$283$	− 29.3390i	− 1.74402i	−0.489488	−	0.872010i	$-0.662816\pi$
$283$	− 29.3390i	− 1.74402i	0.489488	−	0.872010i	$-0.337184\pi$
$284$	3.93344i	0.233407i
$285$	−18.0917	−1.07166
$286$	− 24.2480i	− 1.43381i
$287$	0.870646	0.0513926
$288$	−27.3180	−1.60973
$289$	0	0
$290$	14.0422	0.824585
$291$	32.1639	1.88548
$292$	− 0.654917i	− 0.0383261i
$293$	20.6478	1.20626	0.603129	−	0.797644i	$-0.293920\pi$
$293$	20.6478	1.20626	0.603129	+	0.797644i	$0.293920\pi$
$294$	− 35.8645i	− 2.09166i
$295$	0.484372i	0.0282012i
$296$	1.15425i	0.0670894i
$297$	2.31896	0.134560
$298$	−23.0437	−1.33489
$299$	− 31.4107i	− 1.81653i
$300$	− 5.77226i	− 0.333262i
$301$	− 4.32073i	− 0.249042i
$302$	33.3081	1.91667
$303$	− 22.9270i	− 1.31712i
$304$	−23.9637	−1.37441
$305$	−6.88307	−0.394123
$306$	0	0
$307$	16.3437	0.932787	0.466393	−	0.884577i	$-0.345553\pi$
$307$	16.3437	0.932787	0.466393	+	0.884577i	$0.345553\pi$
$308$	2.10834	0.120134
$309$	12.0574i	0.685921i
$310$	9.97624	0.566613
$311$	− 35.1101i	− 1.99091i	−0.0952411	−	0.995454i	$-0.530362\pi$
$311$	− 35.1101i	− 1.99091i	0.0952411	−	0.995454i	$-0.469638\pi$
$312$	− 7.04056i	− 0.398593i
$313$	31.3134i	1.76994i	0.465651	+	0.884968i	$0.345820\pi$
$313$	31.3134i	1.76994i	−0.465651	+	0.884968i	$0.654180\pi$
$314$	−5.45247	−0.307701
$315$	−1.24261	−0.0700132
$316$	− 12.3193i	− 0.693014i
$317$	− 12.5497i	− 0.704862i	−0.935838	−	0.352431i	$-0.885355\pi$
$317$	− 12.5497i	− 0.704862i	0.935838	−	0.352431i	$-0.114645\pi$
$318$	− 35.6111i	− 1.99697i
$319$	−16.9413	−0.948528
$320$	− 10.1105i	− 0.565195i
$321$	7.19714	0.401705
$322$	5.11906	0.285274
$323$	0	0
$324$	−17.7530	−0.986278
$325$	−4.68778	−0.260031
$326$	39.5358i	2.18968i
$327$	23.8433	1.31854
$328$	− 1.40445i	− 0.0775475i
$329$	− 0.609957i	− 0.0336280i
$330$	13.0529i	0.718537i
$331$	0.497450	0.0273423	0.0136712	−	0.999907i	$-0.495648\pi$
$331$	0.497450	0.0273423	0.0136712	+	0.999907i	$0.495648\pi$
$332$	−22.7597	−1.24910
$333$	6.53146i	0.357922i
$334$	− 8.25640i	− 0.451770i
$335$	− 1.87478i	− 0.102430i
$336$	−3.11207	−0.169777
$337$	− 33.5675i	− 1.82854i	−0.405108	−	0.914269i	$-0.632766\pi$
$337$	− 33.5675i	− 1.82854i	0.405108	−	0.914269i	$-0.367234\pi$
$338$	−18.5843	−1.01085
$339$	−26.9478	−1.46360
$340$	0	0
$341$	−12.0359	−0.651780
$342$	49.9959	2.70347
$343$	− 5.11523i	− 0.276196i
$344$	−6.96979	−0.375786
$345$	16.9086i	0.910328i
$346$	30.2472i	1.62610i
$347$	26.3010i	1.41191i	0.708257	+	0.705955i	$0.249482\pi$
$347$	26.3010i	1.41191i	−0.708257	+	0.705955i	$0.750518\pi$
$348$	−39.1455	−2.09842
$349$	−16.7865	−0.898560	−0.449280	−	0.893391i	$-0.648319\pi$
$349$	−16.7865	−0.898560	−0.449280	+	0.893391i	$0.648319\pi$
$350$	− 0.763976i	− 0.0408362i
$351$	− 4.35161i	− 0.232272i
$352$	20.2630i	1.08002i
$353$	23.4532	1.24829	0.624144	−	0.781309i	$-0.285448\pi$
$353$	23.4532	1.24829	0.624144	+	0.781309i	$0.285448\pi$
$354$	− 2.53090i	− 0.134516i
$355$	−1.71958	−0.0912660
$356$	9.85386	0.522253
$357$	0	0
$358$	30.5316	1.61365
$359$	−18.1568	−0.958279	−0.479139	−	0.877739i	$-0.659051\pi$
$359$	−18.1568	−0.958279	−0.479139	+	0.877739i	$0.659051\pi$
$360$	2.00446i	0.105644i
$361$	32.4000	1.70526
$362$	23.3182i	1.22558i
$363$	12.0104i	0.630382i
$364$	− 3.95637i	− 0.207370i
$365$	0.286310	0.0149862
$366$	35.9648	1.87991
$367$	− 13.6904i	− 0.714635i	−0.933983	−	0.357318i	$-0.883691\pi$
$367$	− 13.6904i	− 0.714635i	0.933983	−	0.357318i	$-0.116309\pi$
$368$	22.3966i	1.16750i
$369$	− 7.94723i	− 0.413716i
$370$	−4.01564	−0.208763
$371$	− 2.51460i	− 0.130552i
$372$	−27.8109	−1.44193
$373$	−10.1594	−0.526035	−0.263018	−	0.964791i	$-0.584718\pi$
$373$	−10.1594	−0.526035	−0.263018	+	0.964791i	$0.584718\pi$
$374$	0	0
$375$	2.52346	0.130311
$376$	−0.983925	−0.0507421
$377$	31.7909i	1.63731i
$378$	0.709190	0.0364768
$379$	4.16411i	0.213896i	0.994265	+	0.106948i	$0.0341078\pi$
$379$	4.16411i	0.213896i	−0.994265	+	0.106948i	$0.965892\pi$
$380$	16.3995i	0.841277i
$381$	− 39.6979i	− 2.03379i
$382$	44.5045	2.27705
$383$	−0.813273	−0.0415563	−0.0207782	−	0.999784i	$-0.506614\pi$
$383$	−0.813273	−0.0415563	−0.0207782	+	0.999784i	$0.506614\pi$
$384$	11.8911i	0.606815i
$385$	0.921703i	0.0469743i
$386$	− 2.94457i	− 0.149875i
$387$	−39.4394	−2.00482
$388$	− 29.1556i	− 1.48015i
$389$	−3.11676	−0.158026	−0.0790131	−	0.996874i	$-0.525177\pi$
$389$	−3.11676	−0.158026	−0.0790131	+	0.996874i	$0.525177\pi$
$390$	24.4942	1.24031
$391$	0	0
$392$	−4.08519	−0.206333
$393$	−10.3250	−0.520828
$394$	− 36.0550i	− 1.81642i
$395$	5.38563	0.270980
$396$	− 19.2448i	− 0.967089i
$397$	− 16.4046i	− 0.823322i	−0.911337	−	0.411661i	$-0.864949\pi$
$397$	− 16.4046i	− 0.823322i	0.911337	−	0.411661i	$-0.135051\pi$
$398$	− 37.0384i	− 1.85657i
$399$	6.67512	0.334174
$400$	3.34250	0.167125
$401$	14.4451i	0.721356i	0.932690	+	0.360678i	$0.117455\pi$
$401$	14.4451i	0.721356i	−0.932690	+	0.360678i	$0.882545\pi$
$402$	9.79593i	0.488576i
$403$	22.5858i	1.12508i
$404$	−20.7826	−1.03397
$405$	− 7.76109i	− 0.385652i
$406$	−5.18102	−0.257130
$407$	4.84469	0.240142
$408$	0	0
$409$	32.2867	1.59648	0.798238	−	0.602342i	$-0.205765\pi$
$409$	32.2867	1.59648	0.798238	+	0.602342i	$0.205765\pi$
$410$	4.88608	0.241306
$411$	− 40.9164i	− 2.01826i
$412$	10.9296	0.538464
$413$	− 0.178714i	− 0.00879396i
$414$	− 46.7266i	− 2.29649i
$415$	− 9.94985i	− 0.488419i
$416$	38.0243	1.86430
$417$	−27.0191	−1.32313
$418$	− 37.0843i	− 1.81385i
$419$	− 18.8776i	− 0.922230i	−0.887340	−	0.461115i	$-0.847450\pi$
$419$	− 18.8776i	− 0.922230i	0.887340	−	0.461115i	$-0.152550\pi$
$420$	2.12974i	0.103921i
$421$	2.06006	0.100401	0.0502006	−	0.998739i	$-0.484014\pi$
$421$	2.06006	0.100401	0.0502006	+	0.998739i	$0.484014\pi$
$422$	14.8666i	0.723693i
$423$	−5.56766	−0.270709
$424$	−4.05632	−0.196993
$425$	0	0
$426$	8.98502	0.435326
$427$	2.53958	0.122899
$428$	− 6.52398i	− 0.315348i
$429$	−29.5511	−1.42674
$430$	− 24.2479i	− 1.16934i
$431$	3.72759i	0.179552i	0.995962	+	0.0897759i	$0.0286151\pi$
$431$	3.72759i	0.179552i	−0.995962	+	0.0897759i	$0.971385\pi$
$432$	3.10281i	0.149284i
$433$	27.9634	1.34383	0.671917	−	0.740626i	$-0.265471\pi$
$433$	27.9634	1.34383	0.671917	+	0.740626i	$0.265471\pi$
$434$	−3.68085	−0.176686
$435$	− 17.1132i	− 0.820517i
$436$	− 21.6132i	− 1.03508i
$437$	− 48.0388i	− 2.29801i
$438$	−1.49600	−0.0714819
$439$	12.5444i	0.598711i	0.954142	+	0.299356i	$0.0967717\pi$
$439$	12.5444i	0.598711i	−0.954142	+	0.299356i	$0.903228\pi$
$440$	1.48680	0.0708806
$441$	−23.1166	−1.10079
$442$	0	0
$443$	−19.9529	−0.947991	−0.473995	−	0.880527i	$-0.657189\pi$
$443$	−19.9529	−0.947991	−0.473995	+	0.880527i	$0.657189\pi$
$444$	11.1944	0.531264
$445$	4.30781i	0.204210i
$446$	−8.14442	−0.385649
$447$	28.0835i	1.32830i
$448$	3.73039i	0.176244i
$449$	20.1861i	0.952640i	0.879272	+	0.476320i	$0.158030\pi$
$449$	20.1861i	0.952640i	−0.879272	+	0.476320i	$0.841970\pi$
$450$	−6.97354	−0.328736
$451$	−5.89483	−0.277577
$452$	24.4273i	1.14896i
$453$	− 40.5927i	− 1.90721i
$454$	7.20540i	0.338166i
$455$	1.72961	0.0810852
$456$	− 10.7677i	− 0.504243i
$457$	37.7391	1.76536	0.882681	−	0.469973i	$-0.155737\pi$
$457$	37.7391	1.76536	0.882681	+	0.469973i	$0.155737\pi$
$458$	9.13479	0.426841
$459$	0	0
$460$	15.3271	0.714630
$461$	38.1740	1.77794	0.888970	−	0.457966i	$-0.151422\pi$
$461$	38.1740	1.77794	0.888970	+	0.457966i	$0.151422\pi$
$462$	− 4.81600i	− 0.224061i
$463$	−13.1481	−0.611044	−0.305522	−	0.952185i	$-0.598831\pi$
$463$	−13.1481	−0.611044	−0.305522	+	0.952185i	$0.598831\pi$
$464$	− 22.6677i	− 1.05232i
$465$	− 12.1581i	− 0.563817i
$466$	− 32.4394i	− 1.50272i
$467$	16.2167	0.750422	0.375211	−	0.926940i	$-0.377570\pi$
$467$	16.2167	0.750422	0.375211	+	0.926940i	$0.377570\pi$
$468$	−36.1136	−1.66935
$469$	0.691720i	0.0319407i
$470$	− 3.42308i	− 0.157895i
$471$	6.64494i	0.306183i
$472$	−0.288285	−0.0132694
$473$	29.2541i	1.34510i
$474$	−28.1405	−1.29254
$475$	−7.16938	−0.328954
$476$	0	0
$477$	−22.9532	−1.05096
$478$	13.6477	0.624233
$479$	2.07499i	0.0948086i	0.998876	+	0.0474043i	$0.0150949\pi$
$479$	2.07499i	0.0948086i	−0.998876	+	0.0474043i	$0.984905\pi$
$480$	−20.4688	−0.934267
$481$	− 9.09123i	− 0.414525i
$482$	− 9.07015i	− 0.413134i
$483$	− 6.23862i	− 0.283867i
$484$	10.8870	0.494865
$485$	12.7460	0.578764
$486$	46.3189i	2.10107i
$487$	24.0260i	1.08872i	0.838851	+	0.544361i	$0.183228\pi$
$487$	24.0260i	1.08872i	−0.838851	+	0.544361i	$0.816772\pi$
$488$	− 4.09662i	− 0.185445i
$489$	48.1824	2.17888
$490$	− 14.2124i	− 0.642051i
$491$	22.3803	1.01001	0.505005	−	0.863116i	$-0.331491\pi$
$491$	22.3803	1.01001	0.505005	+	0.863116i	$0.331491\pi$
$492$	−13.6210	−0.614080
$493$	0	0
$494$	−69.5901	−3.13100
$495$	8.41327	0.378148
$496$	− 16.1042i	− 0.723101i
$497$	0.634459	0.0284594
$498$	51.9891i	2.32969i
$499$	3.69807i	0.165548i	0.996568	+	0.0827742i	$0.0263780\pi$
$499$	3.69807i	0.165548i	−0.996568	+	0.0827742i	$0.973622\pi$
$500$	− 2.28744i	− 0.102297i
$501$	−10.0621	−0.449541
$502$	−8.90965	−0.397657
$503$	− 18.4617i	− 0.823166i	−0.911372	−	0.411583i	$-0.864976\pi$
$503$	− 18.4617i	− 0.823166i	0.911372	−	0.411583i	$-0.135024\pi$
$504$	− 0.739569i	− 0.0329430i
$505$	− 9.08552i	− 0.404300i
$506$	−34.6593	−1.54079
$507$	22.6487i	1.00586i
$508$	−35.9849	−1.59657
$509$	−17.3588	−0.769415	−0.384708	−	0.923039i	$-0.625698\pi$
$509$	−17.3588	−0.769415	−0.384708	+	0.923039i	$0.625698\pi$
$510$	0	0
$511$	−0.105637	−0.00467312
$512$	−31.0910	−1.37404
$513$	− 6.65525i	− 0.293837i
$514$	21.8172	0.962314
$515$	4.77811i	0.210549i
$516$	67.5962i	2.97576i
$517$	4.12980i	0.181628i
$518$	1.48162	0.0650984
$519$	36.8623	1.61808
$520$	− 2.79004i	− 0.122351i
$521$	− 13.9650i	− 0.611819i	−0.952061	−	0.305909i	$-0.901040\pi$
$521$	− 13.9650i	− 0.611819i	0.952061	−	0.305909i	$-0.0989604\pi$
$522$	47.2921i	2.06992i
$523$	−5.59638	−0.244712	−0.122356	−	0.992486i	$-0.539045\pi$
$523$	−5.59638	−0.244712	−0.122356	+	0.992486i	$0.539045\pi$
$524$	9.35929i	0.408862i
$525$	−0.931060	−0.0406348
$526$	28.2127	1.23013
$527$	0	0
$528$	21.0707	0.916984
$529$	−21.8974	−0.952062
$530$	− 14.1120i	− 0.612985i
$531$	−1.63130	−0.0707923
$532$	− 6.05078i	− 0.262335i
$533$	11.0619i	0.479142i
$534$	− 22.5088i	− 0.974052i
$535$	2.85209	0.123307
$536$	1.11582	0.0481960
$537$	− 37.2090i	− 1.60569i
$538$	− 32.3166i	− 1.39327i
$539$	17.1466i	0.738558i
$540$	2.12340	0.0913768
$541$	39.0998i	1.68103i	0.541787	+	0.840516i	$0.317748\pi$
$541$	39.0998i	1.68103i	−0.541787	+	0.840516i	$0.682252\pi$
$542$	20.0137	0.859662
$543$	28.4179	1.21953
$544$	0	0
$545$	9.44863	0.404735
$546$	−9.03740	−0.386765
$547$	29.3984i	1.25698i	0.777816	+	0.628492i	$0.216328\pi$
$547$	29.3984i	1.25698i	−0.777816	+	0.628492i	$0.783672\pi$
$548$	−37.0894	−1.58438
$549$	− 23.1812i	− 0.989351i
$550$	5.17260i	0.220561i
$551$	48.6202i	2.07129i
$552$	−10.0635	−0.428333
$553$	−1.98709	−0.0844995
$554$	− 2.79670i	− 0.118820i
$555$	4.89387i	0.207733i
$556$	24.4919i	1.03869i
$557$	27.9399	1.18385	0.591927	−	0.805992i	$-0.298368\pi$
$557$	27.9399	1.18385	0.591927	+	0.805992i	$0.298368\pi$
$558$	33.5986i	1.42234i
$559$	54.8963	2.32186
$560$	−1.23325	−0.0521145
$561$	0	0
$562$	−32.8362	−1.38511
$563$	11.2994	0.476213	0.238106	−	0.971239i	$-0.423473\pi$
$563$	11.2994	0.476213	0.238106	+	0.971239i	$0.423473\pi$
$564$	9.54256i	0.401814i
$565$	−10.6789	−0.449264
$566$	60.7496i	2.55350i
$567$	2.86354i	0.120257i
$568$	− 1.02345i	− 0.0429430i
$569$	12.1204	0.508114	0.254057	−	0.967189i	$-0.418235\pi$
$569$	12.1204	0.508114	0.254057	+	0.967189i	$0.418235\pi$
$570$	37.4608	1.56906
$571$	− 10.9497i	− 0.458232i	−0.973399	−	0.229116i	$-0.926416\pi$
$571$	− 10.9497i	− 0.458232i	0.973399	−	0.229116i	$-0.0735836\pi$
$572$	26.7871i	1.12003i
$573$	− 54.2378i	− 2.26582i
$574$	−1.80277	−0.0752462
$575$	6.70055i	0.279432i
$576$	34.0508	1.41878
$577$	−9.09883	−0.378789	−0.189395	−	0.981901i	$-0.560653\pi$
$577$	−9.09883	−0.378789	−0.189395	+	0.981901i	$0.560653\pi$
$578$	0	0
$579$	−3.58856	−0.149135
$580$	−15.5126	−0.644126
$581$	3.67111i	0.152303i
$582$	−66.5991	−2.76062
$583$	17.0255i	0.705123i
$584$	0.170404i	0.00705138i
$585$	− 15.7878i	− 0.652745i
$586$	−42.7536	−1.76614
$587$	−11.2991	−0.466362	−0.233181	−	0.972433i	$-0.574913\pi$
$587$	−11.2991	−0.466362	−0.233181	+	0.972433i	$0.574913\pi$
$588$	39.6201i	1.63390i
$589$	34.5422i	1.42329i
$590$	− 1.00295i	− 0.0412907i
$591$	−43.9403	−1.80746
$592$	6.48228i	0.266420i
$593$	−42.8620	−1.76013	−0.880066	−	0.474851i	$-0.842502\pi$
$593$	−42.8620	−1.76013	−0.880066	+	0.474851i	$0.842502\pi$
$594$	−4.80167	−0.197015
$595$	0	0
$596$	25.4568	1.04275
$597$	−45.1388	−1.84741
$598$	65.0394i	2.65966i
$599$	−21.0108	−0.858478	−0.429239	−	0.903191i	$-0.641218\pi$
$599$	−21.0108	−0.858478	−0.429239	+	0.903191i	$0.641218\pi$
$600$	1.50190i	0.0613147i
$601$	19.4501i	0.793387i	0.917951	+	0.396693i	$0.129842\pi$
$601$	19.4501i	0.793387i	−0.917951	+	0.396693i	$0.870158\pi$
$602$	8.94655i	0.364634i
$603$	6.31399	0.257126
$604$	−36.7960	−1.49721
$605$	4.75949i	0.193501i
$606$	47.4729i	1.92845i
$607$	27.4308i	1.11338i	0.830719	+	0.556691i	$0.187929\pi$
$607$	27.4308i	1.11338i	−0.830719	+	0.556691i	$0.812071\pi$
$608$	58.1535	2.35844
$609$	6.31412i	0.255861i
$610$	14.2522	0.577053
$611$	7.74971	0.313520
$612$	0	0
$613$	0.297602	0.0120200	0.00601001	−	0.999982i	$-0.498087\pi$
$613$	0.297602	0.0120200	0.00601001	+	0.999982i	$0.498087\pi$
$614$	−33.8416	−1.36573
$615$	− 5.95468i	− 0.240116i
$616$	−0.548573	−0.0221026
$617$	− 12.6680i	− 0.509995i	−0.966942	−	0.254997i	$-0.917925\pi$
$617$	− 12.6680i	− 0.509995i	0.966942	−	0.254997i	$-0.0820746\pi$
$618$	− 24.9662i	− 1.00429i
$619$	9.75795i	0.392205i	0.980583	+	0.196103i	$0.0628285\pi$
$619$	9.75795i	0.392205i	−0.980583	+	0.196103i	$0.937171\pi$
$620$	−11.0209	−0.442610
$621$	−6.22005	−0.249602
$622$	72.6993i	2.91498i
$623$	− 1.58942i	− 0.0636786i
$624$	− 39.5399i	− 1.58286i
$625$	1.00000	0.0400000
$626$	− 64.8379i	− 2.59144i
$627$	−45.1948	−1.80491
$628$	6.02343	0.240361
$629$	0	0
$630$	2.57297	0.102509
$631$	−40.9574	−1.63049	−0.815244	−	0.579117i	$-0.803397\pi$
$631$	−40.9574	−1.63049	−0.815244	+	0.579117i	$0.803397\pi$
$632$	3.20538i	0.127503i
$633$	18.1179	0.720123
$634$	25.9856i	1.03202i
$635$	− 15.7315i	− 0.624287i
$636$	39.3401i	1.55994i
$637$	32.1763	1.27487
$638$	35.0788	1.38878
$639$	− 5.79132i	− 0.229101i
$640$	4.71221i	0.186267i
$641$	− 3.96498i	− 0.156607i	−0.996930	−	0.0783037i	$-0.975050\pi$
$641$	− 3.96498i	− 0.156607i	0.996930	−	0.0783037i	$-0.0249504\pi$
$642$	−14.9025	−0.588154
$643$	15.4283i	0.608433i	0.952603	+	0.304217i	$0.0983947\pi$
$643$	15.4283i	0.608433i	−0.952603	+	0.304217i	$0.901605\pi$
$644$	−5.65511	−0.222842
$645$	−29.5510	−1.16357
$646$	0	0
$647$	−10.5735	−0.415687	−0.207843	−	0.978162i	$-0.566644\pi$
$647$	−10.5735	−0.415687	−0.207843	+	0.978162i	$0.566644\pi$
$648$	4.61919	0.181459
$649$	1.21001i	0.0474971i
$650$	9.70657	0.380723
$651$	4.48586i	0.175815i
$652$	− 43.6758i	− 1.71048i
$653$	− 14.5705i	− 0.570189i	−0.958499	−	0.285094i	$-0.907975\pi$
$653$	− 14.5705i	− 0.570189i	0.958499	−	0.285094i	$-0.0920250\pi$
$654$	−49.3702	−1.93053
$655$	−4.09160	−0.159872
$656$	− 7.88738i	− 0.307951i
$657$	0.964254i	0.0376191i
$658$	1.26298i	0.0492363i
$659$	−23.7883	−0.926660	−0.463330	−	0.886186i	$-0.653346\pi$
$659$	−23.7883	−0.926660	−0.463330	+	0.886186i	$0.653346\pi$
$660$	− 14.4197i	− 0.561286i
$661$	−9.91502	−0.385650	−0.192825	−	0.981233i	$-0.561765\pi$
$661$	−9.91502	−0.385650	−0.192825	+	0.981233i	$0.561765\pi$
$662$	−1.03003	−0.0400331
$663$	0	0
$664$	5.92189	0.229814
$665$	2.64522	0.102577
$666$	− 13.5241i	− 0.524049i
$667$	45.4408	1.75948
$668$	9.12097i	0.352901i
$669$	9.92562i	0.383747i
$670$	3.88194i	0.149972i
$671$	−17.1946	−0.663790
$672$	7.55218	0.291331
$673$	− 3.97532i	− 0.153237i	−0.997060	−	0.0766186i	$-0.975588\pi$
$673$	− 3.97532i	− 0.153237i	0.997060	−	0.0766186i	$-0.0244124\pi$
$674$	69.5053i	2.67724i
$675$	0.928289i	0.0357299i
$676$	20.5303	0.789627
$677$	− 20.3678i	− 0.782800i	−0.920221	−	0.391400i	$-0.871991\pi$
$677$	− 20.3678i	− 0.782800i	0.920221	−	0.391400i	$-0.128009\pi$
$678$	55.7984	2.14293
$679$	−4.70276	−0.180475
$680$	0	0
$681$	8.78125	0.336498
$682$	24.9217	0.954300
$683$	28.9372i	1.10725i	0.832766	+	0.553625i	$0.186756\pi$
$683$	28.9372i	1.10725i	−0.832766	+	0.553625i	$0.813244\pi$
$684$	−55.2313	−2.11182
$685$	− 16.2144i	− 0.619520i
$686$	10.5917i	0.404391i
$687$	− 11.1326i	− 0.424735i
$688$	−39.1424	−1.49229
$689$	31.9489	1.21716
$690$	− 35.0112i	− 1.33285i
$691$	5.32679i	0.202641i	0.994854	+	0.101320i	$0.0323067\pi$
$691$	5.32679i	0.202641i	−0.994854	+	0.101320i	$0.967693\pi$
$692$	− 33.4145i	− 1.27023i
$693$	−3.10417	−0.117918
$694$	− 54.4591i	− 2.06724i
$695$	−10.7071	−0.406145
$696$	10.1854	0.386075
$697$	0	0
$698$	34.7583	1.31562
$699$	−39.5340	−1.49531
$700$	0.843976i	0.0318993i
$701$	42.2699	1.59651	0.798256	−	0.602318i	$-0.205756\pi$
$701$	42.2699	1.59651	0.798256	+	0.602318i	$0.205756\pi$
$702$	9.01050i	0.340079i
$703$	− 13.9039i	− 0.524396i
$704$	− 25.2571i	− 0.951913i
$705$	−4.17172	−0.157116
$706$	−48.5625	−1.82768
$707$	3.35220i	0.126073i
$708$	2.79592i	0.105077i
$709$	48.3638i	1.81634i	0.418603	+	0.908169i	$0.362520\pi$
$709$	48.3638i	1.81634i	−0.418603	+	0.908169i	$0.637480\pi$
$710$	3.56059	0.133627
$711$	18.1381i	0.680230i
$712$	−2.56390	−0.0960861
$713$	32.2834	1.20902
$714$	0	0
$715$	−11.7105	−0.437949
$716$	−33.7288	−1.26050
$717$	− 16.6325i	− 0.621153i
$718$	37.5957	1.40306
$719$	− 8.24579i	− 0.307516i	−0.988109	−	0.153758i	$-0.950862\pi$
$719$	− 8.24579i	− 0.307516i	0.988109	−	0.153758i	$-0.0491376\pi$
$720$	11.2571i	0.419527i
$721$	− 1.76294i	− 0.0656552i
$722$	−67.0878	−2.49675
$723$	−11.0538	−0.411096
$724$	− 25.7599i	− 0.957360i
$725$	− 6.78165i	− 0.251864i
$726$	− 24.8689i	− 0.922970i
$727$	−6.46089	−0.239621	−0.119811	−	0.992797i	$-0.538229\pi$
$727$	−6.46089	−0.239621	−0.119811	+	0.992797i	$0.538229\pi$
$728$	1.02942i	0.0381527i
$729$	33.1658	1.22836
$730$	−0.592838	−0.0219419
$731$	0	0
$732$	−39.7309	−1.46850
$733$	15.9605	0.589515	0.294758	−	0.955572i	$-0.404761\pi$
$733$	15.9605	0.589515	0.294758	+	0.955572i	$0.404761\pi$
$734$	28.3476i	1.04633i
$735$	−17.3207	−0.638884
$736$	− 54.3507i	− 2.00339i
$737$	− 4.68339i	− 0.172515i
$738$	16.4556i	0.605740i
$739$	0.760943	0.0279918	0.0139959	−	0.999902i	$-0.495545\pi$
$739$	0.760943	0.0279918	0.0139959	+	0.999902i	$0.495545\pi$
$740$	4.43614	0.163076
$741$	84.8096i	3.11556i
$742$	5.20677i	0.191147i
$743$	− 39.3288i	− 1.44283i	−0.692501	−	0.721417i	$-0.743491\pi$
$743$	− 39.3288i	− 1.44283i	0.692501	−	0.721417i	$-0.256509\pi$
$744$	7.23617	0.265291
$745$	11.1290i	0.407733i
$746$	21.0362	0.770191
$747$	33.5097	1.22606
$748$	0	0
$749$	−1.05231	−0.0384506
$750$	−5.22511	−0.190794
$751$	− 33.7907i	− 1.23304i	−0.787339	−	0.616521i	$-0.788542\pi$
$751$	− 33.7907i	− 1.23304i	0.787339	−	0.616521i	$-0.211458\pi$
$752$	−5.52574	−0.201503
$753$	10.8582i	0.395695i
$754$	− 65.8266i	− 2.39726i
$755$	− 16.0861i	− 0.585434i
$756$	−0.783454	−0.0284939
$757$	−23.0663	−0.838359	−0.419180	−	0.907903i	$-0.637682\pi$
$757$	−23.0663	−0.838359	−0.419180	+	0.907903i	$0.637682\pi$
$758$	− 8.62225i	− 0.313174i
$759$	42.2394i	1.53319i
$760$	− 4.26702i	− 0.154781i
$761$	−22.8435	−0.828076	−0.414038	−	0.910260i	$-0.635882\pi$
$761$	−22.8435	−0.828076	−0.414038	+	0.910260i	$0.635882\pi$
$762$	82.1990i	2.97776i
$763$	−3.48618	−0.126208
$764$	−49.1648	−1.77872
$765$	0	0
$766$	1.68397	0.0608445
$767$	2.27063	0.0819876
$768$	26.4052i	0.952814i
$769$	−3.68785	−0.132987	−0.0664936	−	0.997787i	$-0.521181\pi$
$769$	−3.68785	−0.132987	−0.0664936	+	0.997787i	$0.521181\pi$
$770$	− 1.90849i	− 0.0687772i
$771$	− 26.5887i	− 0.957567i
$772$	3.25292i	0.117075i
$773$	5.04027	0.181286	0.0906430	−	0.995883i	$-0.471108\pi$
$773$	5.04027	0.181286	0.0906430	+	0.995883i	$0.471108\pi$
$774$	81.6638	2.93534
$775$	− 4.81801i	− 0.173068i
$776$	7.58606i	0.272324i
$777$	− 1.80565i	− 0.0647773i
$778$	6.45361	0.231373
$779$	16.9178i	0.606141i
$780$	−27.0591	−0.968871
$781$	−4.29569	−0.153712
$782$	0	0
$783$	6.29533	0.224977
$784$	−22.9425	−0.819375
$785$	2.63326i	0.0939852i
$786$	21.3791	0.762567
$787$	13.6490i	0.486534i	0.969959	+	0.243267i	$0.0782191\pi$
$787$	13.6490i	0.486534i	−0.969959	+	0.243267i	$0.921781\pi$
$788$	39.8305i	1.41890i
$789$	− 34.3830i	− 1.22407i
$790$	−11.1516	−0.396754
$791$	3.94010	0.140094
$792$	5.00735i	0.177929i
$793$	32.2663i	1.14581i
$794$	33.9675i	1.20546i
$795$	−17.1983	−0.609961
$796$	40.9169i	1.45026i
$797$	16.6869	0.591081	0.295541	−	0.955330i	$-0.404500\pi$
$797$	16.6869	0.591081	0.295541	+	0.955330i	$0.404500\pi$
$798$	−13.8216	−0.489279
$799$	0	0
$800$	−8.11138	−0.286780
$801$	−14.5081	−0.512619
$802$	− 29.9103i	− 1.05617i
$803$	0.715232	0.0252400
$804$	− 10.8217i	− 0.381652i
$805$	− 2.47224i	− 0.0871352i
$806$	− 46.7664i	− 1.64728i
$807$	−39.3844	−1.38640
$808$	5.40746	0.190234
$809$	− 30.7399i	− 1.08076i	−0.841422	−	0.540379i	$-0.818281\pi$
$809$	− 30.7399i	− 1.08076i	0.841422	−	0.540379i	$-0.181719\pi$
$810$	16.0702i	0.564650i
$811$	− 21.3840i	− 0.750894i	−0.926844	−	0.375447i	$-0.877489\pi$
$811$	− 21.3840i	− 0.750894i	0.926844	−	0.375447i	$-0.122511\pi$
$812$	5.72355	0.200857
$813$	− 24.3908i	− 0.855422i
$814$	−10.0315	−0.351603
$815$	19.0937	0.668825
$816$	0	0
$817$	83.9571	2.93729
$818$	−66.8534	−2.33747
$819$	5.82508i	0.203545i
$820$	−5.39772	−0.188497
$821$	11.9090i	0.415626i	0.978169	+	0.207813i	$0.0666345\pi$
$821$	11.9090i	0.415626i	−0.978169	+	0.207813i	$0.933366\pi$
$822$	84.7220i	2.95502i
$823$	− 19.5943i	− 0.683015i	−0.939879	−	0.341507i	$-0.889063\pi$
$823$	− 19.5943i	− 0.683015i	0.939879	−	0.341507i	$-0.110937\pi$
$824$	−2.84381	−0.0990686
$825$	6.30387	0.219472
$826$	0.370048i	0.0128756i
$827$	− 35.0907i	− 1.22022i	−0.792316	−	0.610111i	$-0.791125\pi$
$827$	− 35.0907i	− 1.22022i	0.792316	−	0.610111i	$-0.208875\pi$
$828$	51.6196i	1.79390i
$829$	−46.3683	−1.61044	−0.805219	−	0.592978i	$-0.797952\pi$
$829$	−46.3683	−1.61044	−0.805219	+	0.592978i	$0.797952\pi$
$830$	20.6023i	0.715116i
$831$	−3.40835	−0.118234
$832$	−47.3958	−1.64315
$833$	0	0
$834$	55.9460	1.93725
$835$	−3.98742	−0.137990
$836$	40.9676i	1.41690i
$837$	4.47251	0.154593
$838$	39.0882i	1.35028i
$839$	24.8903i	0.859309i	0.902993	+	0.429654i	$0.141365\pi$
$839$	24.8903i	0.859309i	−0.902993	+	0.429654i	$0.858635\pi$
$840$	− 0.554142i	− 0.0191197i
$841$	−16.9908	−0.585890
$842$	−4.26559	−0.147002
$843$	40.0176i	1.37828i
$844$	− 16.4233i	− 0.565314i
$845$	8.97524i	0.308758i
$846$	11.5285	0.396357
$847$	− 1.75607i	− 0.0603391i
$848$	−22.7804	−0.782281
$849$	74.0357	2.54090
$850$	0	0
$851$	−12.9947	−0.445453
$852$	−9.92589	−0.340055
$853$	− 28.1063i	− 0.962342i	−0.876627	−	0.481171i	$-0.840212\pi$
$853$	− 28.1063i	− 0.962342i	0.876627	−	0.481171i	$-0.159788\pi$
$854$	−5.25850	−0.179942
$855$	− 24.1455i	− 0.825758i
$856$	1.69749i	0.0580189i
$857$	− 24.5101i	− 0.837250i	−0.908159	−	0.418625i	$-0.862512\pi$
$857$	− 24.5101i	− 0.837250i	0.908159	−	0.418625i	$-0.137488\pi$
$858$	61.1889	2.08896
$859$	12.8979	0.440069	0.220034	−	0.975492i	$-0.429383\pi$
$859$	12.8979	0.440069	0.220034	+	0.975492i	$0.429383\pi$
$860$	26.7871i	0.913432i
$861$	2.19704i	0.0748751i
$862$	− 7.71840i	− 0.262890i
$863$	5.83668	0.198683	0.0993414	−	0.995053i	$-0.468326\pi$
$863$	5.83668	0.198683	0.0993414	+	0.995053i	$0.468326\pi$
$864$	− 7.52970i	− 0.256166i
$865$	14.6078	0.496681
$866$	−57.9014	−1.96757
$867$	0	0
$868$	4.06629	0.138019
$869$	13.4538	0.456390
$870$	35.4349i	1.20136i
$871$	−8.78854	−0.297788
$872$	5.62357i	0.190438i
$873$	42.9266i	1.45285i
$874$	99.4698i	3.36461i
$875$	−0.368961	−0.0124732
$876$	1.65266	0.0558382
$877$	− 18.7846i	− 0.634312i	−0.948373	−	0.317156i	$-0.897272\pi$
$877$	− 18.7846i	− 0.634312i	0.948373	−	0.317156i	$-0.102728\pi$
$878$	− 25.9746i	− 0.876600i
$879$	52.1040i	1.75742i
$880$	8.34991	0.281475
$881$	− 45.7423i	− 1.54110i	−0.637380	−	0.770549i	$-0.719982\pi$
$881$	− 45.7423i	− 1.54110i	0.637380	−	0.770549i	$-0.280018\pi$
$882$	47.8655	1.61171
$883$	6.15932	0.207277	0.103639	−	0.994615i	$-0.466951\pi$
$883$	6.15932	0.207277	0.103639	+	0.994615i	$0.466951\pi$
$884$	0	0
$885$	−1.22229	−0.0410870
$886$	41.3147	1.38800
$887$	− 16.7476i	− 0.562329i	−0.959660	−	0.281165i	$-0.909279\pi$
$887$	− 16.7476i	− 0.562329i	0.959660	−	0.281165i	$-0.0907207\pi$
$888$	−2.91270	−0.0977440
$889$	5.80432i	0.194671i
$890$	− 8.91981i	− 0.298993i
$891$	− 19.3880i	− 0.649522i
$892$	8.99726	0.301251
$893$	11.8522	0.396620
$894$	− 58.1500i	− 1.94483i
$895$	− 14.7452i	− 0.492878i
$896$	− 1.73862i	− 0.0580834i
$897$	79.2637	2.64654
$898$	− 41.7976i	− 1.39480i
$899$	−32.6741	−1.08974
$900$	7.70378	0.256793
$901$	0	0
$902$	12.2059	0.406412
$903$	10.9032	0.362835
$904$	− 6.35579i	− 0.211391i
$905$	11.2615	0.374344
$906$	84.0518i	2.79243i
$907$	− 8.12836i	− 0.269898i	−0.990853	−	0.134949i	$-0.956913\pi$
$907$	− 8.12836i	− 0.269898i	0.990853	−	0.134949i	$-0.0430870\pi$
$908$	− 7.95992i	− 0.264159i
$909$	30.5988	1.01490
$910$	−3.58135	−0.118721
$911$	− 35.6471i	− 1.18104i	−0.807023	−	0.590520i	$-0.798923\pi$
$911$	− 35.6471i	− 1.18104i	0.807023	−	0.590520i	$-0.201077\pi$
$912$	− 60.4714i	− 2.00241i
$913$	− 24.8557i	− 0.822605i
$914$	−78.1431	−2.58474
$915$	− 17.3692i	− 0.574207i
$916$	−10.0913	−0.333427
$917$	1.50964	0.0498528
$918$	0	0
$919$	−24.2398	−0.799596	−0.399798	−	0.916603i	$-0.630920\pi$
$919$	−24.2398	−0.799596	−0.399798	+	0.916603i	$0.630920\pi$
$920$	−3.98799	−0.131480
$921$	41.2428i	1.35900i
$922$	−79.0435	−2.60316
$923$	8.06102i	0.265332i
$924$	5.32031i	0.175025i
$925$	1.93935i	0.0637654i
$926$	27.2246	0.894657
$927$	−16.0920	−0.528531
$928$	55.0085i	1.80574i
$929$	33.4397i	1.09712i	0.836111	+	0.548560i	$0.184824\pi$
$929$	33.4397i	1.09712i	−0.836111	+	0.548560i	$0.815176\pi$
$930$	25.1747i	0.825510i
$931$	49.2097	1.61278
$932$	35.8363i	1.17386i
$933$	88.5989	2.90060
$934$	−33.5786	−1.09873
$935$	0	0
$936$	9.39647	0.307133
$937$	−25.6264	−0.837177	−0.418588	−	0.908176i	$-0.637475\pi$
$937$	−25.6264	−0.837177	−0.418588	+	0.908176i	$0.637475\pi$
$938$	− 1.43228i	− 0.0467657i
$939$	−79.0181	−2.57866
$940$	3.78153i	0.123340i
$941$	− 53.4661i	− 1.74295i	−0.490443	−	0.871473i	$-0.663165\pi$
$941$	− 53.4661i	− 1.74295i	0.490443	−	0.871473i	$-0.336835\pi$
$942$	− 13.7591i	− 0.448296i
$943$	15.8115	0.514892
$944$	−1.61901	−0.0526944
$945$	− 0.342503i	− 0.0111416i
$946$	− 60.5738i	− 1.96943i
$947$	11.7772i	0.382707i	0.981521	+	0.191353i	$0.0612877\pi$
$947$	11.7772i	0.382707i	−0.981521	+	0.191353i	$0.938712\pi$
$948$	31.0873	1.00967
$949$	− 1.34216i	− 0.0435683i
$950$	14.8450	0.481636
$951$	31.6687	1.02693
$952$	0	0
$953$	23.9735	0.776576	0.388288	−	0.921538i	$-0.373067\pi$
$953$	23.9735	0.776576	0.388288	+	0.921538i	$0.373067\pi$
$954$	47.5272	1.53875
$955$	− 21.4934i	− 0.695510i
$956$	−15.0769	−0.487621
$957$	− 42.7506i	− 1.38193i
$958$	− 4.29650i	− 0.138814i
$959$	5.98248i	0.193184i
$960$	25.5135	0.823445
$961$	7.78674	0.251185
$962$	18.8244i	0.606924i
$963$	9.60545i	0.309531i
$964$	10.0199i	0.322720i
$965$	−1.42208	−0.0457783
$966$	12.9178i	0.415622i
$967$	−45.6312	−1.46740	−0.733700	−	0.679473i	$-0.762208\pi$
$967$	−45.6312	−1.46740	−0.733700	+	0.679473i	$0.762208\pi$
$968$	−2.83272	−0.0910471
$969$	0	0
$970$	−26.3919	−0.847394
$971$	58.9182	1.89078	0.945388	−	0.325946i	$-0.105683\pi$
$971$	58.9182	1.89078	0.945388	+	0.325946i	$0.105683\pi$
$972$	− 51.1693i	− 1.64125i
$973$	3.95052	0.126648
$974$	− 49.7486i	− 1.59405i
$975$	− 11.8294i	− 0.378845i
$976$	− 23.0067i	− 0.736425i
$977$	24.7610	0.792176	0.396088	−	0.918213i	$-0.370368\pi$
$977$	24.7610	0.792176	0.396088	+	0.918213i	$0.370368\pi$
$978$	−99.7670	−3.19020
$979$	10.7614i	0.343934i
$980$	15.7007i	0.501540i
$981$	31.8217i	1.01599i
$982$	−46.3410	−1.47880
$983$	9.89686i	0.315661i	0.987466	+	0.157830i	$0.0504499\pi$
$983$	9.89686i	0.315661i	−0.987466	+	0.157830i	$0.949550\pi$
$984$	3.54406	0.112981
$985$	−17.4127	−0.554815
$986$	0	0
$987$	1.53920	0.0489934
$988$	76.8772	2.44579
$989$	− 78.4669i	− 2.49510i
$990$	−17.4206	−0.553664
$991$	− 0.883820i	− 0.0280755i	−0.999901	−	0.0140377i	$-0.995532\pi$
$991$	− 0.883820i	− 0.0280755i	0.999901	−	0.0140377i	$-0.00446850\pi$
$992$	39.0807i	1.24081i
$993$	1.25530i	0.0398356i
$994$	−1.31372	−0.0416687
$995$	−17.8876	−0.567076
$996$	− 57.4332i	− 1.81984i
$997$	29.0009i	0.918467i	0.888315	+	0.459234i	$0.151876\pi$
$997$	29.0009i	0.918467i	−0.888315	+	0.459234i	$0.848124\pi$
$998$	− 7.65728i	− 0.242387i
$999$	−1.80028	−0.0569582

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.d.g.866.4		12
17.2	even	8		85.2.e.a.81.2	yes	12
17.4	even	4		1445.2.a.o.1.5		6
17.8	even	8		85.2.e.a.21.5	✓	12
17.13	even	4		1445.2.a.n.1.5		6
17.16	even	2	inner	1445.2.d.g.866.3		12
51.2	odd	8		765.2.k.b.676.5		12
51.8	odd	8		765.2.k.b.361.2		12
68.19	odd	8		1360.2.bt.d.81.1		12
68.59	odd	8		1360.2.bt.d.1041.1		12
85.2	odd	8		425.2.j.c.149.5		12
85.4	even	4		7225.2.a.z.1.2		6
85.8	odd	8		425.2.j.c.174.5		12
85.19	even	8		425.2.e.f.251.5		12
85.42	odd	8		425.2.j.b.174.2		12
85.53	odd	8		425.2.j.b.149.2		12
85.59	even	8		425.2.e.f.276.2		12
85.64	even	4		7225.2.a.bb.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.5	✓	12	17.8	even	8
85.2.e.a.81.2	yes	12	17.2	even	8
425.2.e.f.251.5		12	85.19	even	8
425.2.e.f.276.2		12	85.59	even	8
425.2.j.b.149.2		12	85.53	odd	8
425.2.j.b.174.2		12	85.42	odd	8
425.2.j.c.149.5		12	85.2	odd	8
425.2.j.c.174.5		12	85.8	odd	8
765.2.k.b.361.2		12	51.8	odd	8
765.2.k.b.676.5		12	51.2	odd	8
1360.2.bt.d.81.1		12	68.19	odd	8
1360.2.bt.d.1041.1		12	68.59	odd	8
1445.2.a.n.1.5		6	17.13	even	4
1445.2.a.o.1.5		6	17.4	even	4
1445.2.d.g.866.3		12	17.16	even	2	inner
1445.2.d.g.866.4		12	1.1	even	1	trivial
7225.2.a.z.1.2		6	85.4	even	4
7225.2.a.bb.1.2		6	85.64	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.07061 q^{2} +2.52346i q^{3} +2.28744 q^{4} +1.00000i q^{5} -5.22511i q^{6} -0.368961i q^{7} -0.595174 q^{8} -3.36786 q^{9} -2.07061i q^{10} +2.49810i q^{11} +5.77226i q^{12} +4.68778 q^{13} +0.763976i q^{14} -2.52346 q^{15} -3.34250 q^{16} +6.97354 q^{18} +7.16938 q^{19} +2.28744i q^{20} +0.931060 q^{21} -5.17260i q^{22} -6.70055i q^{23} -1.50190i q^{24} -1.00000 q^{25} -9.70657 q^{26} -0.928289i q^{27} -0.843976i q^{28} +6.78165i q^{29} +5.22511 q^{30} +4.81801i q^{31} +8.11138 q^{32} -6.30387 q^{33} +0.368961 q^{35} -7.70378 q^{36} -1.93935i q^{37} -14.8450 q^{38} +11.8294i q^{39} -0.595174i q^{40} +2.35972i q^{41} -1.92786 q^{42} +11.7105 q^{43} +5.71425i q^{44} -3.36786i q^{45} +13.8743i q^{46} +1.65317 q^{47} -8.43468i q^{48} +6.86387 q^{49} +2.07061 q^{50} +10.7230 q^{52} +6.81536 q^{53} +1.92213i q^{54} -2.49810 q^{55} +0.219596i q^{56} +18.0917i q^{57} -14.0422i q^{58} +0.484372 q^{59} -5.77226 q^{60} +6.88307i q^{61} -9.97624i q^{62} +1.24261i q^{63} -10.1105 q^{64} +4.68778i q^{65} +13.0529 q^{66} -1.87478 q^{67} +16.9086 q^{69} -0.763976 q^{70} +1.71958i q^{71} +2.00446 q^{72} -0.286310i q^{73} +4.01564i q^{74} -2.52346i q^{75} +16.3995 q^{76} +0.921703 q^{77} -24.4942i q^{78} -5.38563i q^{79} -3.34250i q^{80} -7.76109 q^{81} -4.88608i q^{82} -9.94985 q^{83} +2.12974 q^{84} -24.2479 q^{86} -17.1132 q^{87} -1.48680i q^{88} +4.30781 q^{89} +6.97354i q^{90} -1.72961i q^{91} -15.3271i q^{92} -12.1581 q^{93} -3.42308 q^{94} +7.16938i q^{95} +20.4688i q^{96} -12.7460i q^{97} -14.2124 q^{98} -8.41327i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 12 q^{4} - 12 q^{8} - 4 q^{9} - 8 q^{15} + 4 q^{16} + 28 q^{18} + 24 q^{19} + 16 q^{21} - 12 q^{25} + 24 q^{26} + 8 q^{30} + 12 q^{32} - 16 q^{33} + 16 q^{35} + 20 q^{36} - 24 q^{38} + 16 q^{42}+ \cdots - 44 q^{98}+O(q^{100}) \) 12 * q - 4 * q^2 + 12 * q^4 - 12 * q^8 - 4 * q^9 - 8 * q^15 + 4 * q^16 + 28 * q^18 + 24 * q^19 + 16 * q^21 - 12 * q^25 + 24 * q^26 + 8 * q^30 + 12 * q^32 - 16 * q^33 + 16 * q^35 + 20 * q^36 - 24 * q^38 + 16 * q^42 - 16 * q^43 + 48 * q^47 + 20 * q^49 + 4 * q^50 - 56 * q^52 + 32 * q^59 - 16 * q^60 - 28 * q^64 + 32 * q^66 - 8 * q^67 - 16 * q^70 - 20 * q^72 + 72 * q^76 - 48 * q^77 - 28 * q^81 - 40 * q^83 - 96 * q^86 - 48 * q^87 - 24 * q^89 - 72 * q^93 - 40 * q^94 - 44 * q^98

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